Simplify to lowest terms. $\dfrac{84}{56}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 84 and 56? $84 = 2\cdot2\cdot3\cdot7$ $56 = 2\cdot2\cdot2\cdot7$ $\mbox{GCD}(84, 56) = 2\cdot2\cdot7 = 28$ $\dfrac{84}{56} = \dfrac{3 \cdot 28}{ 2\cdot 28}$ $\hphantom{\dfrac{84}{56}} = \dfrac{3}{2} \cdot \dfrac{28}{28}$ $\hphantom{\dfrac{84}{56}} = \dfrac{3}{2} \cdot 1$ $\hphantom{\dfrac{84}{56}} = \dfrac{3}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{84}{56}= \dfrac{2\cdot42}{2\cdot28}= \dfrac{2\cdot 2\cdot21}{2\cdot 2\cdot14}= \dfrac{2\cdot 2\cdot 7\cdot3}{2\cdot 2\cdot 7\cdot2}= \dfrac{3}{2}$